[求助]急急！请教关于Price index after split 的计算

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2009年sample 2 中有一题：
stock   number fo shares         market price            market price
        outsiding before split    before split day 1     after split day 3
  x       1,000,000                     $10                            $12
  y       5,000,000                     $20                            $19    
  z       4,000,000                     $60                            $22
if stock z complete a three-for-one stock split at the end of day 1, the value of the inex after the split (at the end of day 3)is closed to:
计算是：index before split=(10+20+60)/3=30,new divisor:(10+20+20)/x=30  x=1.67;  index after the split=(12+19+22)/1.67=31.7
请问一下：第一次(day 1) stock z spilit ,index value remains 30,而调整了divisor 是1.67,为什么第二次（day 3）stock 也split,但是没有调整divisor呢？ 而是直接用了1.67呢？
 书上的例子是为使得index value不变,split时调整了divisor。那难道是每次split时都要这样做，index value不就永远不变吗？所以就像这题一样，我就不明白在stock split时,什么时候应该调整。
 
2。还有就是sheweser sample 有一题关于price weighted index.题目我就不写了，我把它的答案解释写上，因为估计在这我肯定有哪里没弄明白地方。
price weighted indexes can be affected in the long run. a stock with a high stock price and split should  have goog chacteristic. if these chacteristic continue, the lower weighting of the stock due to the split will cause the index to have lower long run return than if the stock did not spilt. 红线标出的地方我不太明白。
因为老早看到这就有疑问，快考试了，很急，就一起请教一下大家，不知道我可把我要的疑问说清楚了，真诚的拜托大家帮帮我啊。先谢谢你们啦：）

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关键词：split After Price Index Rice 求助 请教 Index Price split

too difficult to answer

   Let me try answering these two questions in English, as you have to read and answer your CFA problems in English.  

  1. There was actually only ONE stock split for stock z, which happened at the end of day 1. The old index divisor (which was 3) should be updated to the new divisor (5/3=1.67) so that the index values right before and after the split coincide. That is:  (10+20+60)/3 = (10+20+20)/x 

      Note there was no other split between the end of day one and the end of day three. So this new divisor (1.67) should be used to calculate the index value at the end of day 3 (after the split) to get the index value of 31.7.   

      In summary, index divisor is updated whenever there are such events like stock splits.  

2. I’ll explain by an example closely related to Question 1. Suppose the index consists of three stocks x, y, z. Their stock prices at the end of day Dec 31, 2007 were: x = 10, y = 20, and z = 60; their annual returns for 2008 were 5%, 5% and 10% respectively. Let’s calculate the index’s annual return rate under two scenarios.

   A   No stock split for x, y or z during any time in 2008 and on Dec 31, 2007. At the end of 2008, x, y and z had prices of 10.5, 21 and 66 respectively. The index values at the beginning and end of the year 2008 were:       

    IDX1 = (10+20+60)/3 = 30;   IDX2 = (10.5+21+66)/3 = 32.5.  

    So the index’s return for 2008 was  100*(32.5-30)/30= 8.33%

   B   Stock z completed a three-for-one stock split at the end of day Dec 31, 2007. No other split happened in 2008. Stock z’s return for 2008 was still 10%. From Question 1, the new divisor should be 1.67=5/3, applying to the stock index in 2008. Now at the end of 2008, x, y and z’s prices are 10.5, 21 and 22 respectively.

    So IDX2 = (10.5+21+22)/(5/3) = 32.1. (< 32.5)  and the index return for 2008 was  100*(32.1-30)/30 = 7%

  Therefore the lower weighting of the stock z due to the split will cause the index to have lower long run return (7% in scenario B) than if the stock did not split (8.33% in scenario A).

  Hopefully my explanations answer your questions.

[此贴子已经被作者于2009-5-23 6:49:07编辑过]

非常谢谢楼上详细的清楚的回答，我已经明白了。
真的很谢谢

原来at the day 3(after split) stock x y z 分别变成$12 $19 $22，三个stock价值的变化并不是期间三种stock又各自发生了split，而是自身收益率发生了变化，才使得价值与原来的$10 $20 $60相比，发生了变化。括号里面的after split说的还是at the end of day 1，only stock z split.所以在day 1到 day 3 期间，三种stock 没有再发生split，divisor不需要调整，还是用了以前的1.67。
是这样吗？

To viovanessa:

 Yes. Your understanding is correct. There was only one split for z. But the stock prices of x, y and z changes from day to day, regardless of spliting or not.

谢谢你：）